Given: A (h,3) and B (4,1) be the points intersect At right angle at the line 7x – 9y – 19 = 0
To find:
The value of h.
Explanation:
The line 7x − 9y − 19 = 0 can be written as
\(y = \frac{7}{9}x-\frac{19}{9}\)
So, the slope of this line is \(\frac{7}{9}\)
It is given that the line joining the points A (h,3) and B (4,1) is perpendicular to the line 7x − 9y − 19 = 0.
\(\frac{7}{9}\times \frac{1-3}{4-h} = -1\)
⇒ 9h – 36 = -14
⇒ 9h = 22
⇒ h = \(\frac{22}{9}\)
Hence, the value of h is \(\frac{22}{9}\)
